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Convergence analysis and parameter choice for the iterated Arnoldi-Tikhonov method
Multi angle
Authors : Reichel, Lothar (Author of the conference)
CIRM (Publisher )
65D15 - Algorithms for functional approximation
65D32 - Quadrature and cubature formulas
65F60 - Matrix exponential and similar matrix functions (numerical linear algebra) - Numerical computation of matrix exponential and similar matrix functions
CIRM (Publisher )
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Abstract :
This talk is concerned with the inexpensive approximation of expressions of the form $I(f)=$ $v^{T} f(A) v$, when $A$ is a large symmetric positive definite matrix, $v$ is a vector, and $f(t)$ is a Stieltjes function. We are interested in the situation when $A$ is too large to make the evaluation of $f(A)$ practical. Approximations of $I(f)$ are computed with the aid of rational Gauss quadrature rules. Error bounds or estimates of bounds are determined with rational Gauss-Radau or rational anti-Gauss rules.
Keywords : Stieltjes function; rational Gauss quadrature
MSC Codes : Keywords : Stieltjes function; rational Gauss quadrature
65D15 - Algorithms for functional approximation
65D32 - Quadrature and cubature formulas
65F60 - Matrix exponential and similar matrix functions (numerical linear algebra) - Numerical computation of matrix exponential and similar matrix functions
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 07/10/2024 Conference Date : 16/09/2024 Subseries : Research talks arXiv category : Numerical Analysis Mathematical Area(s) : Numerical Analysis & Scientific Computing Format : MP4 (.mp4) - HD Video Time : 00:22:40 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-09-16_Reichel.mp4 
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Information on the Event
Event Title : Numerical Linear Algebra / Algèbre Linéaire NumériqueEvent Organizers : Brezinski, Claude ; Chehab, Jean-Paul ; Redivo-Zaglia, Michela ; Rodriguez, Giuseppe ; Sadok, Hassane Dates : 16/09/2024 - 20/09/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/3064.html
Citation Data
DOI : 10.24350/CIRM.V.20246403Cite this video as: Reichel, Lothar (2024). Convergence analysis and parameter choice for the iterated Arnoldi-Tikhonov method. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20246403 URI : http://dx.doi.org/10.24350/CIRM.V.20246403 |
See Also
- [Multi angle] The linear algebra of Large Language Models / Author of the conference Saad, Yousef.
- [Multi angle] When is the resolvent like a rank one matrix ? / Author of the conference Greenbaum, Anne.
- [Multi angle] What is new in domain decomposition ? / Author of the conference Gander, Martin.
Bibliography
- FROMMER, Andreas et SCHWEITZER, Marcel. Error bounds and estimates for Krylov subspace approximations of Stieltjes matrix functions. BIT Numerical Mathematics, 2016, vol. 56, p. 865-892. - http://dx.doi.org/10.1007/s10543-015-0596-3
- GOLUB, Gene H. et MEURANT, Gérard. Matrices, moments and quadrature with applications. Princeton University Press, 2009. -
- PRANIC, Miroslav S. et REICHEL, Lothar. Rational Gauss quadrature. SIAM Journal on Numerical Analysis, 2014, vol. 52, no 2, p. 832-851. - https://doi.org/10.1137/120902161
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